Nano Energy 27 (2016) 68–77

Contents lists available at ScienceDirect

Nano Energy

http://d2211-28

n CorrE-m

journal homepage: www.elsevier.com/locate/nanoen

On the contact behavior of micro-/nano-structured interface usedin vertical-contact-mode triboelectric nanogenerators

Congrui Jin n, Danial Sharifi Kia, Matthew Jones, Shahrzad TowfighianDepartment of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY 13902, USA

a r t i c l e i n f o

Article history:Received 25 March 2016Received in revised form16 May 2016Accepted 25 June 2016Available online 28 June 2016

Keywords:Energy harvestingTriboelectric nanogeneratorMicrostructureContact interfaceContact mechanicsPyramid array

x.doi.org/10.1016/j.nanoen.2016.06.04955/& 2016 Elsevier Ltd. All rights reserved.

esponding author.ail address: cjin@binghamton.edu (C. Jin).

a b s t r a c t

The triboelectric nanogenerator (TENG) has attracted enormous amount of attention in the researchcommunity in recent years because of its simple design, high energy conversion efficiency, broad ap-plication areas, a wide materials spectrum, and low-temperature easy fabrication. A key factor thatdictates the performance of the TENGs is the surface charge density, which can be taken as a standard tocharacterize the matrix of performance of a material for a TENG. The triboelectric charge density can beimproved by increasing the effective contact area, and in order to increase the contact area in a limiteddevice size, micro-/nano-structures are often designed at the contact surfaces. Expert knowledge incontact mechanics, especially in adhesion and detachment mechanisms of the micro-/nano-structuredinterface, is thus becoming essential for a better understanding of the impact of interfacial design on thepower generation of TENGs. Such an emerging field provides a platform for electrical engineers, chemicalengineers, and mechanicians to share knowledge and build collaborations, which will enable the TENGresearchers to pursue new design philosophies to achieve enhanced performance. In this paper, sys-tematical numerical studies on the adhesive contact at the micro-/nano-structured interface are pre-sented. We use a numerical simulation package in which the adhesive interactions are represented by aninteraction potential and the surface deformations are coupled by using half-space Green's functionsdiscretized on the surface. The results confirmed that the deformation of interfacial structures directlydetermines the pressure-voltage relationship of TENG, and it can be seen that our numerical resultsprovided a better fit with the experimental data than the previous studies.

& 2016 Elsevier Ltd. All rights reserved.

1. Introduction

To scavenge mechanical energy from the ambient environment,in 2012, Wang's group at Georgia Institute of Technology inventeda new method to convert mechanical energy into electricity basedon triboelectrification and electrostatic induction [1], which iscalled the triboelectric nanogenerator (TENG), and since thenTENG has attracted enormous amount of attention in the researchcommunity because of its simple design, high energy conversionefficiency, broad application areas, a wide materials spectrum, andlow-temperature easy fabrication [2–20].

While there are many factors that would affect the poweroutput of the TENGs, such as humidity and the frequency of vi-bration, a key factor that dictates the performance of the TENGs isthe surface charge density, which can be taken as a standard tocharacterize the matrix of performance of a material for a TENG.The triboelectric charge density can be improved by selecting a

proper charging material and by increasing the contact area. Whilethe material issue can be intuitively addressed by combining astrong electron donating material and a strong electron acceptingmaterial, the contact area issue is much more complicated. Toincrease the effective contact area in a limited device size, micro-/nano-structures are often designed at the contact surfaces [21–33].For example, in a recent study to fabricate transparent TENGs [21],three types of regular and uniform polymer patterned arrays, i.e.,line micropatterns, cube micropatterns, and pyramid micro-patterns, were fabricated and compared with flat surfaces with nomicropatterns. A dramatic increase in surface charge density, andtherefore power generation, of the micropatterned surfaces overthe unpatterned surfaces has been found, and the surfaces withpyramid micropatterns has shown the largest effective tribo-electric effect. However, despite the invention of various interfacialstructures, systematical analyses of the underlying phenomena ofcontact interfaces have been surprisingly modest so far. It is stillunclear how the surface structures, such as roughness, dielectricproperties, and the presence of nanostructures, would affect themagnitude of the charge density [34]. More fundamental studies

www.sciencedirect.com/science/journal/22112855www.elsevier.com/locate/nanoenhttp://dx.doi.org/10.1016/j.nanoen.2016.06.049http://dx.doi.org/10.1016/j.nanoen.2016.06.049http://dx.doi.org/10.1016/j.nanoen.2016.06.049http://crossmark.crossref.org/dialog/?doi=10.1016/j.nanoen.2016.06.049&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.nanoen.2016.06.049&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.nanoen.2016.06.049&domain=pdfmailto:cjin@binghamton.eduhttp://dx.doi.org/10.1016/j.nanoen.2016.06.049

C. Jin et al. / Nano Energy 27 (2016) 68–77 69

on this issue are urgently needed.In a recent attempt to investigate the impact of contact pres-

sure on output voltage of TENGs based on deformation of inter-facial structures [35], Seol et al. conducted both experimental andtheoretical analyses of the contact problem of the pyramid arraystructures. Their theoretical analysis has shown that the open-circuit voltage should be proportional to the power of two-thirdsof the applied contact pressure, and on the other hand, their ex-perimental results, however, have shown that the open-circuitvoltage has two distinctive regimes: increment and saturation,depending on the applied pressure, which means that the open-circuit voltage sensitively responds to the pressure change in alow-pressure regime, while the sensitivity significantly decreasedin a high-pressure regime. Despite the elegance and sophisticationof the analysis employed by Seol et al. the work of adhesion of theinterface was not considered as a factor affecting the output vol-tage of TENGs, and thus never used in their analysis. Moreover, noattempt has been made to solve the JKR-type adhesive contact ofthe pyramid array structures. As the experimentally measuredelastic modulus of PDMS was usually only about 0.36–0.87 MPa[36], the contact problem should be considered as JKR-type and sothe influence of Van der Waals forces within the contact zoneshould be taken into account.

Although JKR model predicts high elastic deformation of softand highly adhering materials correctly [37], to our knowledge, theJKR-type adhesive contact for elastic bodies involving more gen-eral shapes, such as pyramids, has not been explored either ana-lytically or numerically. In this paper, numerical studies on theadhesive contact of pyramidal PDMS micro-structures are pre-sented. We use a numerical simulation method in which the ad-hesive interactions are represented by an interaction potential andthe surface deformations are coupled by using half-space Green'sfunctions discretized on the surface. The DMT-type and JKR-type-to-DMT-type transition regimes have been explored by conductingthe simulations using smaller values of Tabor parameters. Aguideline for the design of the interfacial structure is then deducedfrom the systematical analyses.

The paper is organized as follows: In Section 2, mathematicalformulation is presented for the pyramidal adhesive contact pro-blem, and essential dimensionless parameters for the problem aredefined. In Sections 3, 4 and 5, detailed numerical simulation re-sults are presented, as well as the comparison with existing ex-perimental data. The DMT-type and JKR-type-to-DMT-type tran-sition regimes have been explored. Based on the simulation

Fig. 1. A scenario describing the contact pressure dependence of the TENG. Contact eleclayer. If the polymer material contains micro-/nano-structures at its surface, the interfacicharge density, which is resulted from the actual contact area, is dependent on the con

results, the relationship among the voltage between the twoelectrodes, the amount of transferred charges in between, and theseparation distance between the two triboelectric charged layerswas analyzed. Finally, the conclusions drawn from the numericalstudies are summarized in Section 6.

2. Governing equations for the contact problem

A typical state for a vertical contact mode TENG is illustrated inFig. 1. When a constant downward pressure is applied to the TENG,the rigid floating-metal plate and the soft polymer layer with theinterfacial structures come into contact. The total contact areabetween the metal surface and the polymer surface will be de-pendent on the applied pressure and the interfacial structure, i.e.,a stronger pressure will cause a larger deformation of the inter-facial structure, resulting in a larger surface charge density. In thissection, the problem formulation of the adhesive contact problemfor pyramid PDMS micro-structures will be presented. We herefocus on a unit block of the pyramid array with a base length of Lwithin one pitch of a pyramid, a base length of m in a pyramiditself, and inter-pyramid space of L-m, as shown in Fig. 2. Theheight of the pyramid itself is denoted as n.

For surface interaction, the empirical potential often used is theLennard-Jones potential. The Lennard–Jones potential is a pairpotential and it describes the potential energy of interaction Ubetween two non-bonding atoms or molecules based on theirdistance of separation:

( ) ( )ε σ σ( ) = − ( )⎡⎣ ⎤⎦U r r r4 / / 10 0 12 0 6

where ε0 and σ0 are potential parameters and r is the distancebetween the two atoms or molecules. Integrating Eq. (1) over thesurface area, we can obtain the relationship between the localpressure p and the air gap h as follows:

( ) ( )ε

ε ε( ) = − ( )⎡⎣ ⎤⎦p h W h h83 / / 2

ad 9 3

where Wad is the work of adhesion, which is just the tensile forceintegrated over the distance necessary to pull apart the two bodiesand ε is a length parameter equal to the range of the surface in-teraction. For stiff materials, its value should be on the order ofinteratomic spacing, however, for compliant materials, its valueusually becomes much larger [38].

trification occurs when a rigid metal plate comes into contact with a soft polymeral structures are compressed and deformed during the contact, and the triboelectrictact pressure.

Fig. 2. Our analysis focuses on a ×L L unit block of pyramid array structure. A right square pyramid with a base size of ×m m and a height of n has been used in thesimulation. The parameter ho is the initial air gap, i.e., the separation between the rigid metal plate and the soft polymer layer in the absence of applied and adhesive forces,and then due to surface interaction as well as the external loads, the surfaces will deform and the separation will change from ho to h. The parameter α is the displacement(in the z direction) at infinity of the rigid metal plate with respect to the soft polymer layer.

C. Jin et al. / Nano Energy 27 (2016) 68–7770

The Derjaguin's Approximation [39] is then applied to Eq. (2).This approximation relates the force law between two curvedsurfaces to the interaction energy per unit area between twoplanar surfaces, which makes this approximation a very usefultool, since forces between two planar bodies are often much easierto calculate. This approximation is widely used to estimate forcesbetween colloidal particles. Note that Greenwood also adoptedthis approximation in his simulation of the adhesive contact be-tween two inclined surfaces [40]. The separation between the twosurfaces due to the surface interaction as well as the applied load,denoted by h, as shown in Fig. 2, will be expressed by the fol-lowing equation:

∬α ε π( ) = − + + + *( ′ ′) ′ ′

( − ′) + ( − ′) ( )Ωh x y h

Ep x y dx dy

x x y y,

1 ,

30

2 2

where the parameter α is the displacement between the twosurfaces with respect to the zero force position ε=h , which isoften called indentation depth in indentation tests, and the para-meter *E represents the effective elastic contact modulus. For theadhesive contact between two linearly elastic isotropic materialswith Young's modulus Ei and Poisson's ratio νi, where i¼1, 2, *E isdefined as the effective Young's modulus, i.e., if both materialsfeature significant compliances, the compliances add up as thefollowing:

ν ν*

= − + −( )E E E

1 1 14

12

1

22

2

As shown in Fig. 2, the parameter ho in Eq. (3) is the initial airgap written in rectangular coordinates, i.e., the separation of thesurfaces in the absence of applied and adhesive forces. The initialair gap for a right square pyramid with a base size of ×m m and aheight of n, as shown in Fig. 2, can be written as the following:

( ) = (| + | + | − |) − × −

( ) = − × −( )

⎡⎣⎢

⎤⎦⎥

⎡⎣⎢

⎤⎦⎥

⎡⎣⎢

⎤⎦⎥

⎡⎣⎢

⎤⎦⎥

h x ynm

x y x y insidem m m m

h x y n outsidem m m m

,2

,2 2

,2

,2

,2 2

,2 5

0

0

The computational domain is taken as the whole unit block, i.e.,the finite square Ω = [ − ] × [ − ]L L L L/2, /2 /2, /2 . The total normalload f can then be written as follows:

∫ ∫= ( ) ( )Ωf p x y dxdy, 6To implement the formulae into numerical simulation, we then

introduce the following dimensionless variables:

εαε

με ε ε

εε

π ε ε ε

= − = =*

= =

= = = = ¯ =( )

⎜ ⎟

⎜ ⎟ ⎜ ⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎛⎝

⎞⎠

Hh

DmWnE

Uh

X xnm

Y ynm

Pp

WF

n fm W

Nn

L Lnm

1, , , , ,

, ,3

,2

,7

ad

ad ad

2/3

00

2

2

where D is the normalized displacement, i.e. the normalized in-dentation depth in indentation tests. The parameter μ is the socalled Tabor parameter [41]. This parameter, proposed by Tabor in1976, is often used to decide whether the JKR or DMT model wouldbest describe a contact system, as Greenwood [40] concluded thatthe limits of the Maugis-Dugdale model correspond to Tabor'slimits, i.e. the small values of Tabor parameter describe the ma-terial behavior in DMT-type regime, and the large values of theTabor parameter describe the contact behavior for JKR-typeregime.

Then the normalized (Eqs. (2), (3) and 6) can be written asfollows, respectively:

= [( + ) − ( + ) ] ( )− −P H H

83

1 1 89 3

∫ ∫( )

μπ

= − + + [ ( ′ ′) + ] − [ ( ′ ′) + ]

( − ′) + ( − ′)′ ′

Ω

− −

9H D U

H X Y H X Y

X X Y YdX dY

83

, 1 , 10

3/2 9 3

2 2

∬π Ω= ( ) = [ − ¯ ¯ ] × [ − ¯ ¯ ] ( )ΩF P X Y dXdY L L L L1

3, , /2, /2 /2, /2 10

where

( ) = | − | + | + | [ − ] × [ − ]

( ) = [ − ] × [ − ] ( )

U x y X Y X Y inside N N N N

U x y N outside N N N N

, , ,

, 2 , , 11

0

0

Eq. (9) is then solved by a virtual state relaxation (VSR) meth-od: the indentation depth D is gradually increased, and the Hvector obtained from the previous step is used as an initial state

C. Jin et al. / Nano Energy 27 (2016) 68–77 71

for computing H vector in the next step. In each step, we let timeevolve until the final state in equilibrium is reached. This methodaccurately plots all the stable equilibria for each value of D. In allthe simulation cases, we first increase the value of D from mini-mum to the maximum indentation depth to simulate the approachprocess, and then we decrease the value of D back to the minimumto simulate the detachment process. This method has been ex-tensively calibrated and validated in the past few years, showingsuperior capabilities in reproducing and predicting the contactbehavior of adhesive materials in various kinds of contact pro-blems [42–44].

3. Relationship between applied pressure and contact area

In this section, we numerically simulate the approaching pro-cess of the soft micro-structured interface coming into contactwith the rigid metal plate for different geometrical parameters ofthe pyramidal micro-structures. In the analysis conducted by Seolet al. all the geometrical parameters about the pyramid micro-structures are provided, but none of the material parameters areavailable, so the material parameters are assumed here based onour previous experimental experience and the information pro-vided by the existing literature. The Young's modulus of the pyr-amid PDMS micro-structure is assumed to be 0.44 MPa, which iswithin the nominal range of 0.36 to 0.87 MPa [36]. We assumethat ν = 0.5 for the PDMS micro-structures [45], and the metalplate is assumed to be rigid. Based on Eq. (4), we can obtain that

* =E 0.59 MPa. The work of adhesion Wad can be varied from 25 to1000 mJ/m2 [46], and based on our previous experimental resultswe assume that =W 54ad mJ/m2 [44], which is close to the nominalvalue of 100 mJ/m2used by Tafazzoli et al. [46]. For the pyramidal

Fig. 3. Normalized pressure distributions P for pyramidal micro-structures pressed by th(c) D¼6.0, and (d) D¼14.0 during approach. Three groups of samples have been simulaten¼0.7 mm for group A; L¼5.0 mm, m¼2.5 mm, and n¼1.75 mm for group B; and L¼10.0partial contact to full contact for all the three groups of samples.

micro-structures fabricated by Seol et al. because of the nature ofanisotropic etching of silicon with the aid of KOH, the side angle ofthe pyramid is always 54.7°, which means the ratio of n/m is al-ways equal to 0.7. In their experiments, the ratio of m/L is fixed as0.5. In their experiments, three groups of experimental sampleshave been tested, and the geometrical parameters are shown asfollows: L¼2.0 mm, m¼1.0 mm, and n¼0.7 mm for group A;L¼5.0 mm, m¼2.5 mm, and n¼1.75 mm for group B; andL¼10.0 mm, m¼5.0 mm, and n¼3.5 mm for group C. Substituting

* =E 0.59 MPa, =W 54ad mJ/m2, and n/m¼0.7 into the expressionfor Tabor parameter as shown in Eq. (7), we can obtain the re-lationship between the Tabor parameter m and the length para-meter ε. If we assume that μ > 0.5 [43], we can obtain ϵ < 0.37 mm,which is a very reasonable range for compliant materials [38,42].In the following numerical simulations, we assume that the valueof the Tabor parameter is always equal to 0.5.

The relationship among the force, the displacement, and thecontact area will be discussed based on the numerical results.However, as pointed out by Greenwood [40], any criterion to de-fine contact area can be disputable, because the air gap in thiscontext is assumed to be always nonzero. In the current study,Greenwood's definition for contact area will be adopted, i.e., theedge of contact area will be regarded as the location of the tensilepeak stress [40]. In the following discussion, the normalized con-tact region length obtained directly from the numerical simulationis denoted by Λ = | | = | |X Y2 2c c c , where ( X Y,c c) is the coordinatefor the tensile peak stress at the corner of the contact area. Thedimensional contact region length λc is related to the di-mensionless contact region length Λc by Λ λ ε= ( )n m/c c .

Fig. 3 plots the normalized pressure distributions in the unitblock for the pyramid micro-structure pressed by the rigid metalplate for different values of displacement. Positive values of P

e rigid metal plate when the normalized indentation depth: (a) D¼1.0, (b) D¼3.0,d, and the geometrical parameters are shown as follows: L¼2.0 mm, m¼1.0 mm, andmm, m¼5.0 mm, and n¼3.5 mm for group C. The results show the transition from

Fig. 4. (a) The curves for the normalized contact region length Λc versus the normalized displacement D. The three different curves correspond to the numerical simulationresults for group A, B, and C, respectively. The partial-contact-to-full-contact transition happens at D¼1.75 for group A, D¼5.20 for group B, and D¼10.95 for group C,respectively. (b) The curves for the normalized contact region length Λc versus the normalized force F. (c) The curves for the normalized force F versus the normalizeddisplacement D.

C. Jin et al. / Nano Energy 27 (2016) 68–7772

represent compressive forces between surfaces, and the edge ofcontact area can be regarded as the location of the tensile peakstress, which is colored by the deepest shade of blue in the currentcolor scheme. It can be seen that the maximum compressivecontact pressure at the center of the contact area forms a sharppeak. In other words, at the center of the pyramid, the pressure isthe largest because the compression of polymer is most severe,while the pressure becomes smaller as the distance from thecenter increases. It can be seen that when the displacement issmall or the applied pressure is weak, only the top part of thepyramid is compressed, and under this partial-contact condition,the deformed profile sensitively responds to a small change ofpressure. The deformation eventually becomes saturated as theapplied pressure further increases, and the entire area of thepyramid structure is fully in contact with the top metal plate.

Fig. 4(a) plots the normalized contact region length Λc versusthe normalized displacement D. The three different curves corre-spond to the numerical simulation results for group A, B, and C,respectively. It confirms that when the displacement is small, onlythe partial contact is achieved, and the contact area increases withincreasing displacement. The deformation eventually becomessaturated as the displacement further increases. The partial-con-tact-to-full-contact transition happens at D¼1.75 for group A,D¼5.20 for group B, and D¼10.95 for group C, respectively, whichis consistent with the results shown in Fig. 3. Fig. 4(b) plots thenormalized contact region length Λc versus the normalized force F,and Fig. 4(c) plots the normalized force F versus the normalizeddisplacement D, which shows that stronger applied pressure isrequired as displacement is increased. The effect of different pyr-amidal shapes and the effect of using different Tabor parametershave been discussed in the Supplementary information.

Fig. 5. The relationship between the contact pressure and the open-circuit voltage.The three different curves correspond to the numerical simulation results for groupA, B, and C, respectively. The experimental data provided by Seol et al. are alsoplotted for comparison.

4. Relationship between pressure and open-circuit voltage

Our analysis so far has been focusing on a single unit block. Thetotal contact area of the device can be obtained by multiplying thecontact area of a unit block λc2 and the total number of unit blocks.For the pyramid structure with a base length of L, assuming thatthe total sample size is equal to S, the number of unit blocks willbe S/L2, and then the total contact area will be λc2S/L2. Althoughsome recent studies [47–50] suggest that each charged surfaceactually has surface charge distributions fluctuating rapidly be-tween positive and negative values, like a random “mosaic”, in-stead of having uniform surface charge distributions, we heresimply adopt the assumption made by Seol et al. and the vastmajority of studies [51,52] that the total triboelectric charge can beobtained by multiplying the total contact area and the uniform

surface charge density σ , which is a parameter for intrinsic ma-terial property. The open-circuit voltage VOC can then be de-termined by the total amount of triboelectric charge σλ S L/c2 2 andparasitic capacitance CP. The parasitic capacitance is formed by thepolymer layer. The fixed triboelectric charges at the polymer sur-face serves as a virtual electrode which makes a pair with actualmetal electrode attached to the polymer layer. The value of CP isdetermined by total thickness of the polymer layer T, dielectricconstant of the polymer εr , and total device area S. The resultantrelationship can be shown as follows:

σλ σλε ε

σε ε

λ= =( )

=( )

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟V

SL C

SL S T

TL/ 12

OCc

P

c

r rc

2

2

2

20 0

22

where ε = × −8.85 100 12 F/m is the vacuum permittivity. It can beseen that VOC is a function of material parameters σ and εr ,structural parameters T and L, and contact area from a unit blockλc2; and VOC is independent on total device area S.

The relationship between λc and f has been analyzed in theprevious section, and based on Eq. (12), we can derive the re-lationship between VOC and f. We assume that εr is equal to 2.40[53], the thickness of the polymer layer is 400 mm (provided bySeol et al. through private communication), and the uniform sur-face charge density σ is equal to 5.84 mC/m2. Fig. 5 presents therelationship between the pressure f/L2 and the open-circuit vol-tage VOC. The three different curves correspond to the numerical

Fig. 6. Theoretical model for a conductor-to-dielectric vertical-contact-mode TENG.

C. Jin et al. / Nano Energy 27 (2016) 68–77 73

simulation results for group A, B, and C, respectively. The experi-mental data provided by Seol et al. are also plotted for comparison.

Three important tendencies are found from the results. 1) Asmall-size pyramid array (e.g. L¼2 mm sample) produces a largerVOC than a large-size pyramid array (e.g. L¼10 mm sample) in thepartial-contact range, as a consequence of the larger density ofcontact points of the small-size structure array. When the appliedpressure is so low that only the peak of the pyramid is in contact,the number of contact points determines the total contact area.This result implies that the high density of structures with smallunit size, such as vertical nanowire array, will present an excellentperformance in terms of the ultralow pressure application. 2) Asshown in Eq. (12), when the values of σ , εr , T, and L are fixed, the

open-circuit voltage solely depends on ( )λLc22 . Under the full-con-tact condition, we have λ ≈ mc . Since in the experiments, the ratioof m/L is 0.5 for all the three groups of samples, and thus we cansee that the open-circuit voltages are the same for all the threecases once the full contact condition has been achieved. 3) It canbe seen that our numerical results provided a better fit with theexperimental data than the previous studies, especially when theapplied pressure is large, and our model accurately predicts thetransition from partial contact to full contact.

The notable discrepancy between the experimental data andnumerical results in the range of small applied pressure is prob-ably caused by the fact that when the value of Tabor parameter isnot very small as in this cases involving PDMS, the contact andseparation between two surfaces do not occur smoothly, and thereare sudden jumping in or jumping out of contact behaviors [40,42–44]. When two bodies move closer from a large separation, aturning point exists indicating the sudden jumping-on of con-tacting surfaces when they move infinitesimally closer. This sig-nificantly complicates the experimental measurements to accu-rately determine the contact area and the initial force. This issue iswell known, and it also exists in the nanoindentation tests onPDMS [54–58]. As discussed by Kaufman and Klapperich [56],“Adhesion models, such as Johnson-Kendall-Roberts (JKR), can besuccessfully applied to both quasi-static and dynamic na-noindentation experiments to accurately determine elastic mod-ulus values that demonstrate this jump-into-contact behavior. In aprototypical indent, the indenter tip senses a negative load as itapproaches the sample such that a minimum force is seen on theloading curve prior to the applied load increasing. The minimumforce on the loading curve is then defined as the jump-into-con-tact and zero displacement position”. Wang et al. also discussedthis issue, and according to them, many nanoindentation studiesignored this initial contact adhesion force effect, reporting only thepositive load portion of the load–displacement curve [55].

5. Real-time output of TENG

In this section, the impact of the deformation of interfacialstructures on the real-time power output of TENG will be in-vestigated. The theoretical model for a conductor-to-dielectricvertical-contact-mode TENG is shown in Fig. 6. It shows that themotion of the top metal plate can be modeled as a spring-masssystem, and thus the equation of motion of the top metal plate isshown as follows:

¨ ( ) + ( ) = ( ) = ( ) + ( ) ( )y tkM

y tP t S

MP t S F t

M 13e t a e

where S is the area of the top plate, M is the mass of the top plate,Pt(t) is the total pressure on the top plate, and ke is the equivalentstiffness. The total force Pt(t)S is the summation of the appliedforce Pa(t)S and the electrostatic force Fe(t). For high frequency

input pressures, some amount of damping can be added to theequation.

Assume that the amount of transferred charges between thetwo electrodes is denoted as Q(t), the voltage between the twoelectrodes is denoted as V(t), and the distance between the topmetal plate and the PDMS layer is denoted as d(t). Note that theinitial separation is d(0)¼d0. Remember that the thickness of thepolymer layer is T, and dielectric constant of the polymer is εr .From the Gauss theorem, the electric field strength at each regionis given by = −

ε ε( )EPDMS

Q tS r0

and = σε

− ( ) + ( )EairQ t A t

S 0, respectively [18].

The voltage between the two electrodes can then be written asfollows:

ε εσ

ε( ) = + ( ) = − ( ) + ( ) + ( ) ( )

( )

⎛⎝⎜

⎞⎠⎟V t E T E d t

Q tS

Td t

A t d tS 14

PDMS airr0 0

Note that A(t) is the contact area λ ( )tc2 S/L2, which is differentfrom the area of the top plate S, because of the existence of thepyramid micro-structures.

In addition to the applied force, the top plate also experienceselectrostatic force, as the top plate and the PDMS layer can beconsidered as a parallel-plate capacitor of area A(t) and separationd(t). The capacitance can be calculated as ( ) = ε ( )

( )C t A t

d t0 , and the

amount of energy stored in the charged capacitor is( ) = ( ) ( )W t C t V t1

22. The electrostatic force can then be obtained as

( ) = ∂ ( )∂ ( )

= ( ) ( ) ∂ ( )∂ ( )

+ ∂ ( )∂ ( )

( )( )

F tW ty t

C t V tV ty t

C ty t

V t12 15

e2

When the TENG is working, the top plate and the PDMS layerwill either be in contact or not in contact. When they are not incontact, we have ( ) = − ( )d t d y t0 . In general cases that a vertical-contact-mode TENG is connected to an arbitrary resistor R, theoutput properties can be estimated by combining Eq. (14) withOhm's law:

( )ε εσ

ε( ) = ( ) = ( ) = − ( ) + − ( ) + ( )[ − ( )]

⎛⎝⎜

⎞⎠⎟ 16V t I t R R

dQ tdt

Q tS

Td y t

A t d y tSr0

00

0

The power can then be obtained as W(t)¼ I(t)V(t). Two specialcases of the open-circuit condition and short-circuit condition canfirst be analyzed. At open-circuit condition, there is no chargetransfer, which means that Q is equal to zero. Therefore, the open-circuit voltage VOC is given by

σε

( ) = ( )[ − ( )]( )

V tA t d y t

S 17OC0

0

At short-circuit condition, V is equal to zero. Therefore, the

C. Jin et al. / Nano Energy 27 (2016) 68–7774

transferred charge QSC and current ISC are, respectively, given by

σε

( ) = ( )[ − ( )]+ − ( ) ( )

Q tA t d y t

T d y t/ 18SC

r

0

0

σ εε

( ) = ( ) = − ( )̇ ( )

[ + − ( )] ( )I t

dQ tdt

A t y t TT d y t

// 19

SCSC r

r 02

Substituting Eq. (16) into Eq. (15) gives

( )

εε ε

σε ε

σε

εε ε

σε

( ) = ( )− ( )

− ( ) + − ( ) +( )[ − ( )] ( ) − ( )

+ ( )[ − ( )]

− ( ) + − ( ) +( )[ − ( )]

⎛⎝⎜

⎛⎝⎜

⎞⎠⎟

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎛⎝⎜

⎞⎠⎟

⎞⎠⎟ 20

F tA t

d y tQ tS

Td y t

A t d y tS

Q tS

A tS

A t

d y t

Q tS

Td y t

A t d y tS

12

er

r

0

0 00

0

0 0 0

0

02 0

00

0

2

Therefore, when the top plate and the PDMS layer are not incontact, the governing equations can be obtained as follows:

σ

( ) = − ( )ϵ ϵ

+ − ( )

+( ) − ( )

ϵ

( ) + ( ) = ( ) + ( )( )

⎧

⎨

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎛⎝⎜

⎞⎠⎟

⎡⎣ ⎤⎦

RdQ t

dtQ tS

Td y t

A t d y t

S

y tkM

y tP t S F t

M 21

r

e a e

00

0

0

When the top plate and the PDMS layer are in contact, we have( ) =y t d0. Therefore, the voltage can be written as

ε ε( ) = − ( )

( )

⎛⎝⎜

⎞⎠⎟V t

Q tS

T22r0

In this case, the surface charges on each surface are close en-ough to cancel each other out. Thus, the electrostatic force is equalto zero when they are in contact.

We introduce the following dimensionless variables:

( )

σ

γ γε

γε

γ σε

¯ = ¯ (¯) = ( ) (¯) = ( ) ¯ (¯) = ( ) ¯ (¯) = ( )

= ( ) = = = ( )23

tt

M ky t

y td

P tP t Sd k

Q tQ t

SF t

F td k

A tS

d M k

SRTd

A td k

/, , , ,

,/

, ,

ea

a

ee

e

e

e

r e

0 0 0

1 20

03

04

2

0 0

Then Eq. (21) can be written as follows:

( )γ γ γ¯ (¯)¯ = − ¯ (¯)( + − ¯ (¯)) + − ¯ (¯)¯ (¯) + ¯ (¯) = ¯ (¯) + ¯ (¯) ( )

⎧⎨⎪⎩⎪

⎡⎣ ⎤⎦dQ tdt

Q t y t y t

y t y t P t F t

1 1

24a e

2 3 1

where ( )( )γ γ γ γ¯ (¯) = − ¯ (¯)( + − ¯ (¯)) + [ − ¯ (¯)] ¯ (¯) − +− ¯ (¯)⎜⎛⎝F t Q t y t y t Q t1 1e y t4

11 3 1 1

)( )γ γ− ¯ (¯)( + − ¯ (¯)) + [ − ¯ (¯)][ − ¯ (¯)] Q t y t y t1 1y t12 1 3 1 22 .To study the real time output of TENG, we first focus on a

special case when A(t)¼S, i.e., the contact area will not increasewith the applied force. This happens when there are no micro-/nano-structures at the interface, i.e., the interface is flat, or theforce is so large that the deformation of the micro-/nano-struc-tures has been saturated. In the experiments conducted in Ref.[24], to trigger the TENG, a mechanical shaker was used to applyimpulse impact, and then open-circuit voltage and short-circuitcurrent were measured to characterize the TENG's electric per-formance. It has been shown that with a contacting force of 10 N,the TENG can produce Isc ranging from 160 μA to 175 μA, and VOCranging from 200 V to 210 V. To simulate these results, we sub-stitute the material parameters into (Eqs. (23) and 24) and thenumerical results are shown in Fig. 7. Most of the material para-meters were provided by Ref. [24], and so we have M¼13.45 g[24], R¼1 M Ω [24], S¼38.71 cm2 [24], T¼10 mm [24], and d0¼1 mm [24]. The spring constant is assumed to be 1278.88 N/m[24], and since four springs are used in TENG [24], we have ke¼4k¼5.12 kN/m. We also assume that ε = 2.40r [53] and σ

¼1.77 mC/m2. Fig. 7 plots the input pressure, the displacement ofthe top plate, the velocity of the top plate, the charge, the current,the voltage, the short-circuit current, the open-circuit current, andthe power under a square wave input of pressure with an ampli-tude of 10 N/38.71 cm2 and a frequency of 5 Hz. It can be seen thatour numerical results agree very well with the experimental data[24].

In the experiments conducted in Ref. [35], the contact areaincreases with increasing applied pressure until the deformation issaturated. Since the relationship between VOC and Pa(t) in thestatic case has been provided, we can derive the relationship be-tween the total contact area A(t) and the pressure Pa(t). Since mostof the material parameters were not provided by Ref. [35], we hereassume that M¼13.45 g [24], R¼1 M Ω [24], S¼4.00 cm2 [35],T¼400 mm (provided by Seol et al. through private communica-tion), ke¼5.12 kN/m [24], ε = 2.40r [53], σ ¼5.84 mC/m2, and d0¼0.1 mm. Fig. 8(a) plots the curves for the total contact area A(t)versus the pressure Pa(t). The three different curves correspond tothe numerical simulation results for group A, B, and C, respectively.Then, as in the experiments, we assume that pressures from10 kPa to 150 kPa with a step of 10 kPa are sequentially applied inform of a square wave with a frequency of 2 Hz. To simulate theseresults, we substitute the relationship between the total contactarea and the applied pressure into (Eqs. (23) and 24), and thenumerical results for real time output of VOC for group A are shownin Fig. 8(b), which match the experimental data very well. It can beseen that the deformation of interfacial structures directly de-termines the pressure-voltage relationship of TENG. The real timeoutput of VOC during the continuous deformation of PDMS struc-tures are discussed in Supplementary information.

6. Concluding remarks

In this paper, numerical studies on the adhesive contact of thepyramidal micro-/nano-structures used in the vertical-contact-mode triboelectric nanogenerators are presented. We use a nu-merical simulation method in which the adhesive interactions arerepresented by an interaction potential and the surface deforma-tions are coupled by using half-space Green's functions discretizedon the surface. The results confirmed that the deformation of in-terfacial structures directly determines the pressure-voltage re-lationship of TENG. The transition from partial contact to fullcontact has been analyzed in great details. It can be seen that ournumerical results provide a better fit with the experimental datathan previous studies. This numerical simulation package can beeasily extended to include other types of micro-/nano-structures,such as line micropatterns and cube micropatterns. It can also beused to simulate the contact behavior of randomly rough surfaces,but the simulation will be based on a system consisting of billionsof surface points for height distribution, which is quite involvedand necessitates a large computer.

It can be concluded that the interfacial structure of the TENGshould be carefully designed with consideration of a specific targetapplication, and our simulation package provides a powerful toolto predict the contact behavior of the designed micro-/nano-structures. The design of the interfacial structure can be custo-mized to provide controllable pressure sensitivity and sensingrange, which can be another potential advantage when the TENGis designed for a self-powered pressure sensor.

Besides the TENG research, this work has many other applica-tions. For example, instrumented indentation, using preferablypyramid indenters such as Vickers, Berkovich and Knoop, hasproved to be very useful in testing small material volumes [59].Although instrumented indentation has been in use for about 30years, many fundamental issues remain unclear, such as the

Fig. 7. (a) The input pressure as a square wave with an amplitude of 10 N/38.71 cm2 and a frequency of 5 Hz; (b) the displacement of the top plate; (c) the velocity of the topplate; (d) the charge; (e) the current; (f) the voltage; (g) the short-circuit current; (h) the open-circuit current; and (i) the power. It can be seen that our numerical resultsagree very well with the experimental data [24].

Fig. 8. (a) The curves for the total contact area A(t) versus the pressure Pa(t). The three different curves correspond to the numerical simulation results for group A, B, and C,respectively. (b) The numerical results for real-time output of VOC for group A, assuming that pressures from 10 kPa to 150 kPa with a step of 10 kPa are sequentially appliedin form of a square wave with a frequency of 2 Hz. It can be seen that the deformation of interfacial structures directly determines the pressure-voltage relationship of TENG.

C. Jin et al. / Nano Energy 27 (2016) 68–77 75

C. Jin et al. / Nano Energy 27 (2016) 68–7776

explicit relations between the normal applied load and the depthof penetration, details of the contact area shapes, the contactpressure distributions, and the effect of geometrical imperfections,etc. [60]. The current study will be very useful in the investigationof those issues.

Acknowledgment

This work is supported by start-up funds provided by the De-partment of Mechanical Engineering at State University of NewYork at Binghamton. Prof. Yang-Kyu Choi at Korea Advanced In-stitute of Science and Technology is thanked for kindly providingthe material parameters used in the experiments.

Appendix A. Supporting information

Supplementary data associated with this article can be found inthe online version at http://dx.doi.org/10.1016/j.nanoen.2016.06.049.

References

[1] F.R. Fan, Z.Q. Tian, Z. Lin Wang, Nano Energy 1 (2012) 328–334.[2] Y. Yang, G. Zhu, H. Zhang, J. Chen, X. Zhong, Z.H. Lin, Y. Su, P. Bai, X. Wen, Z.

L. Wang, ACS Nano 7 (2013) 9461–9468.[3] P. Bai, G. Zhu, Z. Lin, Q. Jing, J. Chen, G. Zhang, ACS Nano 7 (2013) 1–3.[4] X.S. Zhang, M. Di Han, R.X. Wang, B. Meng, F.Y. Zhu, X.M. Sun, W. Hu, W. Wang,

Z.H. Li, H.X. Zhang, Nano Energy 4 (2014) 123–131.[5] G. Zhu, Y.S. Zhou, P. Bai, X.S. Meng, Q. Jing, J. Chen, Z.L. Wang, Adv. Mater. 26

(2014) 3788–3796.[6] M.L. Seol, J.H. Woo, S.B. Jeon, D. Kim, S.J. Park, J. Hur, Y.K. Choi, Nano Energy 14

(2015) 201–208.[7] G. Cheng, L. Zheng, Z.-H. Lin, J. Yang, Z. Du, Z.L. Wang, Adv. Energy Mater. 5

(2014) 1401452.[8] P.K. Yang, Z.H. Lin, K.C. Pradel, L. Lin, X. Li, X. Wen, J.H. He, Z.L. Wang, ACS Nano

9 (2015) 901–907.[9] S. Wang, X. Mu, Y. Yang, C. Sun, A.Y. Gu, Z.L. Wang, Adv. Mater. 27 (2015)

240–248.[10] J. Yang, J. Chen, Y. Liu, W. Yang, Y. Su, Z.L. Wang, ACS Nano 8 (2014) 2649–2657.[11] L. Lin, Y. Xie, S. Wang, W. Wu, S. Niu, X. Wen, Z.L. Wang, L.I.N.E.T. Al, ACS Nano

7 (2013) 8266–8274.[12] Z. Lin, G. Zhu, Y.S. Zhou, Y. Yang, P. Bai, J. Chen, Z.L. Wang, Angew. Chem. 52

(2013) 5169–5173.[13] Y. Yang, Y. Zhou, H. Zhang, Y. Liu, S. Lee, Adv. Mater. 25 (2013) 6594–6601.[14] T.C. Hou, Y. Yang, H. Zhang, J. Chen, L.J. Chen, Z. Lin Wang, Nano Energy 2

(2013) 856–862.[15] W. Tang, Y. Han, C. Han, C. Gao, X. Cao, Adv. Mater. 27 (2015) 272–276.[16] M. Taghavi, A. Sadeghi, B. Mazzolai, L. Beccai, V. Mattoli, Appl. Surf. Sci. 323

(2014) 82–87.[17] J. Chen, G. Zhu, J. Yang, Q. Jing, P. Bai, W. Yang, X. Qi, Y. Su, Z.L. Wang, ACS Nano

9 (2014) 105.[18] S. Niu, S. Wang, L. Lin, Y. Liu, Y.S. Zhou, Y. Hu, Z.L. Wang, Energy Environ. Sci. 6

(2013) 3576.[19] Y.S. Zhou, Y. Liu, G. Zhu, Z. Lin, C. Pan, Q. Jing, Nano Lett. 13 (2013) 2771–2776.[20] V. Nguyen, R. Yang, Nano Energy 2 (2013) 604–608.[21] F.R. Fan, L. Lin, G. Zhu, W. Wu, R. Zhang, Z.L. Wang, Nano Lett. 12 (2012)

3109–3114.[22] S. Wang, L. Lin, Z.L. Wang, Nano Lett. 12 (2012) 6339–6346.[23] G. Cheng, Z.H. Lin, L. Lin, Z.L. Du, Z.L. Wang, ACS Nano 7 (2013) 7383–7391.[24] G. Zhu, Z.H. Lin, Q. Jing, P. Bai, C. Pan, Y. Yang, Y. Zhou, Z.L. Wang, Nano Lett. 13

(2013) 847–853.[25] Z.H. Lin, Y. Xie, Y. Yang, S. Wang, G. Zhu, Z.L. Wang, ACS Nano 7 (2013)

4554–4560.[26] Z.H. Lin, G. Cheng, Y. Yang, Y.S. Zhou, S. Lee, Z.L. Wang, Adv. Funct. Mater. 24

(2014) 2810–2816.[27] G. Zhu, C. Pan, W. Guo, C.Y. Chen, Y. Zhou, R. Yu, Z.L. Wang, Nano Lett. 12

(2012) 4960–4965.[28] W. Yang, J. Chen, G. Zhu, J. Yang, P. Bai, Y. Su, ACS Nano 7 (2013) 11317–11324.[29] J. Chen, G. Zhu, W. Yang, Q. Jing, P. Bai, Y. Yang, T.C. Hou, Z.L. Wang, Adv. Mater.

25 (2013) 6094.[30] C.K. Jeong, K.M. Baek, S. Niu, T.W. Nam, Y.H. Hur, D.Y. Park, G. Hwang, M. Byun,

Z.L. Wang, Y.S. Jung, K.J. Lee, Nano Lett. 14 (2014) 7091.[31] D. Kim, S.B. Jeon, J.Y. Kim, M.L. Seol, S.O. Kim, Y.K. Choi, Nano Energy 12 (2015)

331–338.[32] K.Y. Lee, J. Chun, J.-H. Lee, K.N. Kim, N.-R. Kang, J.-Y. Kim, M.H. Kim, K.-S. Shin,

M.K. Gupta, J.M. Baik, S.-W. Kim, Adv. Mater. 26 (2014) 5037–5042.

[33] M.-L. Seol, J.-H. Woo, D.-I. Lee, H. Im, J. Hur, Y.-K. Choi, Small 10 (2014)3887–3894.

[34] Z.L. Wang, Faraday Discuss. 176 (2014) 447–458.[35] M.-L. Seol, S.-H. Lee, J.-W. Han, D. Kim, G.-H. Cho, Y.-K. Choi, Nano Energy 17

(2015) 63–71.[36] D. Armani, C. Liu, N. Aluru, in: Proceedings of IEEE MEMS’99, Orlando, FL, 7–21

January, 1999, pp. 222–227.[37] K. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985.[38] T. Tang, A. Jagota, C.Y. Hui, M. Chaudhury, J. Adhes. 82 (2006) 1–26.[39] B.V. Derjaguin, Untersuchungen über die Reibung und Adhäsion, IV. Theorie

des Anhaftens kleiner Teilchen. Kolloid Z., 69, 1934, pp. 155–164.[40] J.A. Greenwood, Proc. R. Soc. A 453 (1997) 1277–1297.[41] D. Tabor, J. Colloid Interface Sci. 58 (1977) 2–13.[42] C. Jin, J. Adhes. Sci. Technol. 30 (2016) 1223–1242.[43] C. Jin, A. Jagota, C.-Y. Hui, J. Phys. D: Appl. Phys. 44 (2011) 405303.[44] C. Jin, K. Khare, S. Vajpayee, S. Yang, A. Jagota, C.-Y. Hui, Soft Matter 7 (2011)

10728.[45] B. Wang, S. Krause, Macromolecules 20 (1987) 201.[46] A. Tafazzoli, C. Pawashe, M. Sitti, in: Proceedings of IEEE International Con-

ference on Robotics and Automation, 2006, pp. 263–268.[47] M.M. Apodaca, P.J. Wesson, K.J.M. Bishop, M.A. Ratner, B.A. Grzybowski, An-

gew. Chem. Int. Ed. 49 (2010) 946–949.[48] H.T. Baytekin, Z. Patashinski, M. Branicki, B. Baytekin, S. Soh, B. Grzybowski,

Science 333 (2011) 308–312.[49] B. Baytekin, H.T. Baytekin, B.A. Grzybowski, J. Am. Chem. Soc. 134 (2012)

7223–7226.[50] K. Brormann, K. Burger, A. Jagota, R. Bennewitz, J. Adhes. 88 (2012) 589.[51] L.H. Lee, J. Electrostat. 32 (1994) 1–29.[52] F. Saurenbach, D. Wollmann, B.D. Terris, F. Diaz, Langmuir 8 (1992) 1199–1203.[53] Y. Yu, X. Wang, Extrem. Mech. Lett. (2016), http://dx.doi.org/10.1016/j.

eml.2016.02.019.[54] J.C. Kohn, D.M. Ebenstein, J. Mech. Behav. Biomed. Mater. 20 (2013) 316–326.[55] Z. Wang, A.A. Volinsky, N.D. Gallant, J. Appl. Polym. Sci. 132 (2015) 41384.[56] J.D. Kaufman, C.M. Klapperich, J. Mech. Behav. Biomed. Mater. 2 (2009) 312.[57] Y.F. Cao, D.H. Yang, W. Soboyejoy, J. Mater. Res. 20 (2005) 2004.[58] D.M. Ebenstein, K.J. Wahl, J. Colloid Interface Sci. 298 (2006) 652–662.[59] A. Fischer-Cripps, Nanoindentation, Springer, New York, 2002.[60] A.E. Giannakopoulos, J. Mech. Phys. Solids 54 (2006) 1305–1332.

Congrui Jin received a B. S. degree in Electrical En-gineering from Nankai University. She earned her M. S.in Mechanical Engineering from the University of Al-berta in 2009 and received the pH.D. with a major inSolid Mechanics and a minor in Applied Mathematicsat Cornell University in 2012. She then became apostdoctoral research scientist at Oak Ridge NationalLaboratory and then Northwestern University. From2015, she has been an assistant professor at State Uni-versity of New York at Binghamton. Her research in-terests include contact mechanics, adhesion science,and dynamics and vibrations.

Danial Sharifi Kia received his B. S. in Mechanical En-gineering from K. N. Toosi University of Technology,Iran. He is currently a pH.D. student in MechanicalEngineering at State University of New York at Bin-ghamton. His research interests include computationalbiomechanics, nonlinear solid mechanics and implantand prosthesis design.

Matthew Jones received his B. S. and M. S. in Me-chanical Engineering from Binghamton University in2014 and 2015, respectively. During his time as agraduate student, his research mainly focused on thedesign and fabrication of triboelectric nanogenerators.He worked toward deriving a more accurate theoreticalmodel of triboelectric generators. He also conductednanofabrication, specifically the use of photo-lithography to form nanostructures on the surface ofpolymer materials. He is currently working as a productdevelopment engineer in the automotive industry.

http://dx.doi.org/10.1016/j.nanoen.2016.06.049http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref1http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref1http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref2http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref2http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref2http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref3http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref3http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref4http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref4http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref4http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref5http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref5http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref5http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref6http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref6http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref6http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref7http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref7http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref8http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref8http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref8http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref9http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref9http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref9http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref10http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref10http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref11http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref11http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref11http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref12http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref12http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref12http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref13http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref13http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref14http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref14http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref14http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref15http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref15http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref16http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref16http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref16http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref17http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref17http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref18http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref18http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref19http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref19http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref20http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref20http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref21http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref21http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref21http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref22http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref22http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref23http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref23http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref24http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref24http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref24http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref25http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref25http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref25http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref26http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref26http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref26http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref27http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref27http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref27http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref28http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref28http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref29http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref29http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref30http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref30http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref31http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref31http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref31http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref32http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref32http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref32http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref33http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref33http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref33http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref34http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref34http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref35http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref35http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref35http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref36http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref37http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref37http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref38http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref38http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref39http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref39http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref40http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref40http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref41http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref42http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref42http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref43http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref44http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref44http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref44http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref45http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref45http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref45http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref46http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref46http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref46http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref47http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref48http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref48http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref49http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref49http://dx.doi.org/10.1016/j.eml.2016.02.019http://dx.doi.org/10.1016/j.eml.2016.02.019http://dx.doi.org/10.1016/j.eml.2016.02.019http://dx.doi.org/10.1016/j.eml.2016.02.019http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref51http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref51http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref52http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref53http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref54http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref55http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref55http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref56http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref57http://refhub.elsevier.com/S2211-2855(16)30233-6/sbref57

C. Jin et al. / Nano Energy 27 (2016) 68–77 77

Shahrzad Towfighian received her B. S. degree fromAmirkabir University of Technology, Iran and earnedher pH.D. degree from the University of Waterloo, Ca-nada in 2011. She has been an assistant professor atMechanical Engineering Department of BinghamtonUniversity since fall 2013. Her research interests in-clude micro-electro-mechanical systems (MEMS) andenergy harvesting. Her research on energy harvesting isfocused on converting mechanical vibrations to elec-tricity through piezoelectric and triboelectric trans-duction methods. She is especially interested inscavenging human passive motions for biomedical ap-

plications. Some recent activities include instrumented

knee implants and self-powering ECG sensors from breathing motions using tri-boelectric energy harvesters.

On the contact behavior of micro-/nano-structured interface used in vertical-contact-mode triboelectric nanogeneratorsIntroductionGoverning equations for the contact problemRelationship between applied pressure and contact areaRelationship between pressure and open-circuit voltageReal-time output of TENGConcluding remarksAcknowledgmentSupporting informationReferences